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How do you judge the risks and benefits of new medical treatments, or of lifestyle choices? With a finite health care budget, how do you decide which treatments should be made freely available on the NHS? Historically, decisions like these have been made on the basis of doctors' individual experiences with how these treatments perform, but over recent decades the approach to answering these questions has become increasingly rational. Statistics and maths are used not just to test new treatments, but also to measure such fuzzy terms as quality of life, and to figure out which treatments provide most "health for money".

While the decisions of health authorities affect all our lives, the underlying calculations are rarely discussed in the media. To explore these difficult decisions and the role of maths in evidence-based medicine, we have put together a package of six articles, three podcasts, a career interview and a classroom activity.

Mathematical mind reading on pi day

To celebrate pi day on the 14th of March 2010, a mathematician and a magician will attempt to pull off what promises to be the world's largest live online magic trick — and you can join in via Twitter!

The mathematician James Grime and the magician Brian Brushwood will exploit the magical power of mathematics to read your mind over the internet. Visit the pi day magic website for instructions on how to join up to this record-breaking attempt, and watch this space for an
explanation of how it's done to be published after the event.

New treatments and drugs are tested extensively before they come on the market using randomised controlled trials (RCTs). We talk to David Spiegelhalter (Winton Professor of the Public Understanding of Risk), Sheila Bird (Professor at the Medical
Research Council Biostatistics Unit), and Nigel Hawkes (journalist and director of Straight Statistics) about why RCTs are used and how they test if a new treatment works. You can also read an accompanying article.

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Calling all algebraic artists!

Everyone has the chance to create mathematical beauty as part of a competition during the Cambridge Science Festival. As part of the Imaginary exhibition of beautiful mathematical images and artwork taken from algebraic
geometry and differential geometry, visitors (both real and virtual) can create their own mathematical art.

By downloading the SURFER program, anyone can create images of algebraic surfaces by simple equations using the three spatial coordinates of x, y and z. For example, the equation x2 + y2 + z2 = 1 results in a sphere.

The competition requires creativity, intuition and mathematical skill in order to create equations yourself or to change given equations to produce beautiful images. The images are easily generated with the SURFER programme, and you can then upload your artwork to the competition gallery by 20 March. Everybody is invited to take part, including group entries from classes and families. The
entries will be judged by a distinguished panel including Sir Christopher Frayling (Royal College of Art and Arts Council England) and Conrad Shawcross (sculptor and artist-in-residence at the Science Museum, London).

So good luck to all aspiring artists, and if you need some inspiration why not browse through the Plus articles on maths and art.

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What does mathematics feel like?

If you have ever wondered what it feels like to do mathematics, take a look at the series of beautiful short films produced by the mathematics department at the University of Bristol. Chrystal Cherniwchan, Azita Ghassemi and Jon Keating interviewed over 60 mathematicians, asking them to describe the emotional aspects of maths research.
The discussions range from the role of creativity and beauty in maths, to what it feels like to pursue the wrong research path, and the eureka moment of discovering mathematical truth. You can view them all on the Mathematical Ethnographies site.

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Maths in a minute — Achilles and the tortoise

Achilles and a tortoise are competing in a 100m sprint. Confident in his victory, Archilles lets the tortoise start 10m ahead of him. The race starts, Achilles zooms off and the tortoise starts bumbling along. When Achilles has reached the point A from where the tortoise started, it has crawled along by a small distance to point B. In a flash Achilles reaches B, but the tortoise is already at
point C. When he reaches C, the tortoise is at D. When he's at D, the tortoise is at E. And so on. He's never going to catch up with the tortoise, so he has no chance of winning the race.

Something's wrong here, but what? Let's assume that Achilles is ten times faster than the tortoise and that both are moving at constant speed. In the times it takes Achilles to travel the first 10m to point A, the tortoise, being ten times slower, has only moved by 1m to point B. By the time Achilles has travelled 1m to point B, the tortoise has crawled along by 0.1m to point C. And so on.
After n such steps the tortoise has travelled

1+1/10+1/100+1/1000+ .... +1/10(n-1) metres.

And this is where the flaw of the argument lies. The tortoise will never cover the 90m it has to run using steps like these, no matter how many of them it takes. In fact, the distance covered in this way will never exceed 10/9=1.111... metres. This is because the geometric progression

1+1/10+1/100+1/1000+...

converges to 10/9. Since the tortoise is travelling at constant speed, it covers this distance in a finite time, and it's precisely when it's done that that Achilles overtakes it.

This problem is known as one of Zeno's paradoxes, after the ancient Greek philosopher Zeno, who used paradoxes like this one to argue that motion is just an illusion.